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arXiv · 1812.04209

Trigonometric integrable tops from solutions of associative Yang-Baxter equation

T. Krasnov·A. Zotov
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Abstract

We consider a special class of quantum non-dynamical $R$-matrices in the fundamental representation of ${\rm GL}_N$ with spectral parameter given by trigonometric solutions of the associative Yang-Baxter equation. In the simplest case $N=2$ these are the well-known 6-vertex $R$-matrix and its 7-vertex deformation. The $R$-matrices are used for construction of the classical relativistic integrable tops of the Euler-Arnold type. Namely, we describe the Lax pairs with spectral parameter, the inertia tensors and the Poisson structures. The latter are given by the linear Poisson-Lie brackets for the non-relativistic models, and by the classical Sklyanin type algebras in the relativistic cases. In some particular cases the tops are gauge equivalent to the Calogero-Moser-Sutherland or trigonometric Ruijsenaars-Schneider models.

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BibTeXRIS

T. Krasnov, A. Zotov. 2018-12-11. Trigonometric integrable tops from solutions of associative Yang-Baxter equation. https://doi.org/10.1007/s00023-019-00815-1

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